As terms for representing a coupled state of signals between cores in a general sense, the term “coupled state” and the term “imperfect coupled state” are used. As terms for representing the inter-core coupled state in a strict sense, the term “perfect coupled state” and the term “uncoupled state” are known.
The term “coupled state” represents a coupled state in which the coupling efficiency is almost 1, and the term “imperfect coupled state” represents a coupled state in which the coupling efficiency is smaller than 1 but not perfectly zero.
The term “perfect coupled state” represents a coupled state in which the coupling efficiency is perfectly 1, and the term “uncoupled state” represents a coupled state in which the coupling efficiency is close to zero, being a value at which the coupling efficiency is unmeasurable.
In the field of a multicore fiber, the term “coupled multicore fiber” and the term “uncoupled multicore fiber” are used. In this case, coupling in the “coupled multicore fiber” indicates that the inter-core coupled state corresponds to the “coupled state” in a general sense, and coupling in the “uncoupled multicore fiber” indicates that the inter-core coupled state corresponds to the “imperfect coupled state” in a general sense.
The present invention employs the terms used in the field of the multicore fiber. That is, being “uncoupled” in the “uncoupled multicore fiber” is not the state of “uncoupled” in the strict sense, but indicates being “imperfect coupled” in the general sense, which means the coupled state with the coupling efficiency being smaller than 1 but not perfectly zero.
For spatial division multiplexed transmission by the use of the multicore fiber, there are known configurations in which multiple single mode cores are accommodated in one optical fiber, such as those disclosed in the Non-Patent Document 1 and the Non-Patent Document 2.
To keep individual cores in the uncoupled state, the following configurations are known: a configuration in which the cores are placed with a sufficient core center interval, a configuration in which cores with different propagation constants are used so that the imperfect coupled state is maintained even though the cores are placed close enough, and a configuration in which a separation layer or an air hole is provided between the cores.
FIG. 32 illustrates models in a manner being the simplest for describing the inter-core coupled state of the multicore fiber.
An attempt to configure an uncoupled multicore fiber, by use of identical cores with the same propagation constant, requires to separate the cores significantly so as to avoid cross talk therebetween, and this makes it difficult to increase the core density. Accordingly, the uncoupled multicore fiber employs non-identical cores with different propagation constants to establish the multicore fiber.
FIG. 32A) illustrates independent waveguides of non-identical cores with different propagation constants β0(1) and β0(2). FIG. 32B illustrates uncoupled waveguides of non-identical cores, being two types with different propagation constants. A multi-core fiber using two types of non-identical cores which have different propagation constants β0(1) and β0(2) forms the uncoupled waveguides.
It is to be noted here that non-identical cores represent cores with different propagation constants, and identical cores represent cores with the same propagation constant.
Propagation constants may be made different by using various values as parameters, such as a refractive index difference, a core diameter, and a refractive index profile. FIG. 33 illustrates one example of different propagation constants. FIG. 33A illustrates a configuration example of the multicore fiber made up of a triangular arrangement of three types of cores with different propagation constants, and the figures from FIG. 33B to FIG. 33D illustrate examples in which the propagation constants of the cores are made different, by using various refractive index differences, core diameters, and refractive index profile.
The core shown in FIG. 33B has the core diameter of 2a-1, the refractive index of n1-1, and the cladding refractive index of n2-1. The core shown in FIG. 33C has the core diameter of 2a-2, the refractive index of n1-2, and the cladding refractive index of n2-2. The core shown in FIG. 33D has the core diameter of 2a-3, the peak refractive index of n1-3, and the refractive index profile with the cladding refractive index of n2-3.
The inventors of the present invention proposed a heterogeneous uncoupled multicore fiber (MCF) that suppresses inter-core coupling and accommodates cores at high density, by using multiple single mode cores with various relative refractive index differences Δ (Non Patent Document 3).
The relative refractive index difference Δ is defined as the following, when the refractive index of the core is assumed as n1, and the refractive index of the first cladding is assumed as n2:Δ=(n12−n22)/2n12 In the case where the relative refractive index difference Δ between the core and the first cladding is extremely small relative to 1 (Δ is much less than 1), it is expressed as (n1−n2)/n1 according to weakly guiding approximation.
The relative refractive index difference Δc between the first cladding and the second cladding is defined as the following, when the refractive index of the first cladding is assumed as n2, and the refractive index of the second cladding is assumed as n3:Δc=(n22−n32)/2n22 
FIG. 33A illustrates the multicore fiber made up of a large number of cores that have different propagation constants, being arranged in a triangular lattice pattern. In this example, the core center interval is Λ between neighboring non-identical cores having different propagation constants, and the core center interval is D between identical cores having the same propagation constant. Note that, in the triangular lattice pattern arrangement using three types of cores, there is the relation of D=√3×Λ between the core center interval Λ and the core center interval D, based on the geometrical shape of the arrangement, Λ representing the distance between non-identical cores and D representing the distance between identical cores.
With reference to FIG. 34 to FIG. 37, an explanation will be provided as to a procedure for designing an uncoupled multicore fiber made up of the non-identical cores. FIG. 34 and FIG. 35 illustrate the case of high refractive index difference where the relative refractive index difference is large between the core and the cladding in the non-identical core, and FIG. 36 and FIG. 37 illustrate the case of low refractive index difference where the relative refractive index difference is small between the core and the cladding of the non-identical core. Those examples illustrate the case where Δ=1.10% to 1.30% is assumed as the high refractive index difference, and the case where Δ=0.3% to 0.4% is assumed as the low refractive index difference.
The multi-core fiber has a problem of cross talk caused by coupling phenomenon, that is, signal light leaks mutually into the cores within the optical fiber.
For the same core center interval, the cross talk between identical cores is higher than the cross talk between non-identical cores, and for the same cross talk level, the identical core center interval D is larger than the non-identical core center interval Λ. If the identical core center interval D is determined in the triangular arrangement of cores of three types in such a manner that a defined cross talk level is obtained between the identical cores, and this may allow a propagation constant difference to be defined between the non-identical cores, so that the cross talk between non-identical cores is sufficiently lower than the defined cross talk level.
Conventional procedures for designing the uncoupled multicore fiber made up of non-identical cores is; firstly, calculating the identical core center interval D based on the cross talk that is defined between the identical cores, and then, calculating the non-identical core center interval Λ according to geometric relations in the core arrangement.
FIG. 34 illustrates a procedure for determining the identical core center interval D. In FIG. 34A, the distance between the identical cores with the same relative refractive index difference Δ is assumed as D. A coupling length lc between identical cores is 5,000 km, when the cross talk is set to be equal to or lower than −30 dB between identical cores for the propagation distance of 100 km as a required condition in designing. Assuming a coupling coefficient between two cores as κ, the cross talk caused by the coupling between the identical cores is represented by normalized power sin2(κL) that is transferred from one core to the other core after propagating only by a certain distance L. The coupling length lc is defined as a length which renders the normalized power transferred from one core to the other core to be 1.0, and therefore, it is expressed as lc=π/(2κ).
FIG. 34B illustrates the relations between the coupling length lc and the identical core center interval D, where the core diameter 2a=5 μm and the relative refractive index difference Δ is 1.10%, 1.15%, 1.20%, 1.25%, and 1.30%. The relations as shown in FIG. 34B indicates that when the relative refractive index difference Δ is 1.20%, the identical core center interval D, which satisfies the condition that coupling length lc=5,000 km or longer, is 40 μm.
FIG. 35 illustrates the cross talk between non-identical cores and an arrangement thereof. In FIG. 35A, the non-identical cores are arranged at the non-identical core center interval Λ that is determined from the identical core center interval D. FIG. 35B illustrates the power coupling efficiency (also referred to as the maximum power transfer efficiency) of the non-identical cores. The power coupling efficiency represents the cross talk between non-identical cores. This figure illustrates the cross talk by the power coupling efficiency F, with respect to the relative refractive index difference Δ2 in each case where the relative refractive index difference Δ1 is 1.15%, 1.20%, and 1.25%. As illustrated, the power coupling efficiency (maximum power transfer efficiency) F represents the cross talk caused by the coupling between the non-identical cores.
The power coupling efficiency (maximum power transfer efficiency) F between two non-identical cores is expressed by the following formula:F=1/[1+(β1−β2)2/(2κ)2]In the above formula, κ represents the inter-core coupling coefficient, βn represents the propagation constant of the core n (Non Patent Document 3).
FIG. 35B illustrates the cases where the non-identical core center interval Λ is 10 μm, 15 μm, and 20 μm, indicating that the larger is the non-identical core center interval Λ, the smaller is the cross talk. If a gap between the relative refractive index differences Δ is 0.05% in the case where the non-identical core center interval Λ is 23 μm, the cross talk is equal to or lower than −80 dB, and it is possible to assume that the cross talk value of −30 dB being defined as the set value is satisfied.
When the identical core center interval D is 40 μm, the non-identical core center interval Λ in the triangular lattice arrangement is 23 μm (=40/√3), and the non-identical core center interval Λy in a rectangular lattice arrangement is 28.3 μm (=40×√3/2). FIGS. 35C and D illustrate, respectively, an example of the triangular lattice arrangement where 19 cores are arranged and an example of the rectangular lattice arrangement where 12 cores are arranged, in the case where the fiber diameter is set to be 125 μm.
In the case of low refractive index difference where the relative refractive index difference is small between the core and the cladding of the non-identical core, similar to the case of high refractive index difference, the coupling length lc between identical cores is 5,000 km, when the cross talk between identical cores is set to be equal to or lower than −30 dB for the propagation distance of 100 km as a required condition in designing.
FIG. 36A illustrates the distance D between the identical cores having the same relative refractive index difference Δ, and FIG. 36B illustrates the relations between the coupling length lc and the identical core center interval D. Here, the core diameter is assumed as 2a=9 μm, and results are shown respectively for the relative refractive index differences Δ, being 0.3%, 0.325%, 0.35%, 0.375%, and 0.40%. According to the relations as shown in FIG. 36B, when the relative refractive index difference is 0.35%, the identical core center interval D is 70 μm, which satisfies the coupling length lc=5,000 km or more.
FIG. 37 illustrates the cross talk between the non-identical cores, and the core arrangement thereof. In FIG. 37A, the non-identical cores are arranged, keeping the non-identical core center interval Λ therebetween, the distance being determined by the identical core center interval D. FIG. 37B illustrates the power coupling efficiency (maximum power transfer efficiency) of the non-identical cores. This figure illustrates the cross talk by the power coupling efficiency F with respect to the relative refractive index difference Δ2, in each case where the relative refractive index difference Δ1 is 0.325%, 0.350%, and 0.375%.
FIG. 37B illustrates the cases where the non-identical core center interval Λ is 20 μm, 30 μm, and 40 μm, indicating that the larger is the non-identical core center interval Λ, the smaller is the cross talk. If a gap between the relative refractive index differences Δ is 0.025% in the case where the non-identical core center interval Λ is 40 μm, the cross talk is equal to or lower than −80 dB, and therefore it is confirmed that the cross talk value of −30 dB being defined as the set value is satisfied.
When the identical core center interval D is 70 μm, the non-identical core center interval Λ is 40 μm (=70/√3) in the triangular lattice arrangement, and the non-identical core center interval Λy is 52.0 μm (=70×√3/2) in the rectangular lattice arrangement. FIGS. 37C and D illustrate, respectively, an example of the triangular lattice arrangement where 7 cores are arranged and an example of the rectangular lattice arrangement where 6 cores are arranged, in the case where the fiber diameter is set to be 125 μm.
The core arrangement in the heterogeneous uncoupled multicore fiber is based on the periodic arrangement of a symmetric configuration such as the triangular arrangement or the rectangular arrangement. According to the aforementioned examples, the identical core center interval for the cross talk of the same level is approximately three times larger than the non-identical core center interval. Therefore, it is suggested to raise the number of the non-identical core types so as to increase the core density (Non Patent Documents 4 and 5).
FIG. 38 illustrates the cores become denser, along with raising the number of types of non-identical core. FIG. 38A illustrates an example in which nine types of various cores are arranged. A cross-section of the core usually has a circular shape, but in this figure, the cores are represented by symbols having polygonal shapes being displayed for easily identifying the respective non-identical cores. In this arrangement example, the center of gravity of the lattice points in the triangular lattice arrangement is added as a placing position, and nine types of cores are arranged.
FIG. 38B illustrates the number of cores being able to be accommodated within the radius R. If nine types of non-identical cores as shown in FIG. 38B are used, the number of cores being able to be accommodated is 55 for the case where R/D is 1.25. It is to be noted here that R represents the diameter of a range for arranging the cores, and D represents the identical core center interval. In FIG. 38B, the symbols from “a” to “e” represent, respectively, single type core, two types of non-identical cores, three types of non-identical cores, four types of non-identical cores, and eight types of non-identical cores, which are arranged.
In the case where the refractive index difference is high where the relative refractive index difference is large between the core and the cladding in the non-identical core, as shown in FIG. 39A, 19 cores are able to be accommodated in the example where three types of non-identical cores are arranged, whereas, as shown in FIG. 39B, 55 cores are able to be accommodated in the example where nine types of non-identical cores are arranged. Therefore, raising the number of types of the non-identical cores allows the cores to be denser.
As a configuration for increasing the core density, other than raising the number of types of the non-identical cores as described above, there is suggested a configuration that a portion with low refractive index, referred to as “trench”, is formed in the portion corresponding to the cladding between adjacent cores (Non Patent Documents 6 and 7).